Enter the tension force of the elevator motor, the elevator mass, and the acceleration due to gravity into the calculator to determine the Elevator Acceleration.
- All Acceleration Calculators
- Pulley Acceleration Calculator
- Pulley Force Calculator
- Elevator Capacity Calculator
- All Physics Calculators
Elevator Acceleration Formula
The calculator uses one of three formulas depending on which tab you select. All results are returned in m/s², with conversions to ft/s² and g.
Cable force mode:
a = T/m - g
Scale reading mode:
a = F_scale/m - g
Speed change mode:
a = (v_f - v_i)/t
- a = elevator acceleration (m/s²). Positive is upward.
- T = upward cable or motor tension (N)
- m = mass of the elevator car plus its load (kg)
- g = acceleration due to gravity (m/s²), default 9.80665
- F_scale = apparent weight read on a scale inside the car (N)
- v_i, v_f = initial and final velocity (m/s)
- t = time taken for the velocity change (s)
The cable force tab applies Newton's second law to the car: the net upward force is T minus the weight mg, divided by the mass. The scale reading tab uses the same logic from the rider's perspective, where the scale reads m(g+a). The speed change tab skips forces entirely and uses the kinematic definition of average acceleration.
Typical Values and Result Interpretation
Use these tables to sanity check your input values and to interpret the output the calculator produces.
| Elevator type | Typical acceleration | In g |
|---|---|---|
| Low-rise residential | 0.6 to 0.9 m/s² | 0.06 to 0.09 g |
| Standard office building | 1.0 to 1.2 m/s² | 0.10 to 0.12 g |
| High-rise express | 1.5 to 2.0 m/s² | 0.15 to 0.20 g |
| Ultra high-speed (skyscraper) | 2.0 to 2.5 m/s² | 0.20 to 0.25 g |
| Free fall (cable cut) | -9.81 m/s² | -1.00 g |
| Sign of a | What it means | Apparent weight |
|---|---|---|
| a > 0 | Accelerating up or slowing down while descending | Heavier than mg |
| a = 0 | At rest or constant speed | Equal to mg |
| a < 0 | Accelerating down or slowing while rising | Lighter than mg |
| a = -g | Free fall | Zero (weightless) |
Example Problems
Example 1: Cable tension. An elevator car with passengers has a mass of 800 kg. The cable pulls upward with 8,400 N. Using a = T/m - g:
a = 8400 / 800 - 9.81 = 10.5 - 9.81 = 0.69 m/s². The car accelerates upward at about 0.07 g.
Example 2: Bathroom scale in an elevator. A 70 kg person stands on a scale that reads 770 N. Using a = F/m - g:
a = 770 / 70 - 9.81 = 11.0 - 9.81 = 1.19 m/s² upward. If the same scale read 630 N, the acceleration would be -0.81 m/s², meaning the elevator is accelerating downward.
FAQ
Why is my acceleration negative? Negative means the acceleration vector points downward. This happens when the elevator starts moving down, when it slows to a stop at the top floor, or when the cable tension is less than the car's weight.
What gravity value should I use? The default 9.80665 m/s² is the standard value and is fine for nearly all problems. Use 32.174 ft/s² if you are working in US units.
Does the cable force include the counterweight? The T in the formula is the net upward force applied to the car. In a real system the motor only supplies the difference between car weight and counterweight, but for this calculator just use the resultant upward force on the car.
How is apparent weight related to acceleration? A scale reads the normal force pushing up on the rider, which equals m(g+a). If a is positive the scale reads more than your true weight; if a is negative it reads less. At a = -g the scale reads zero.
